An Exact Solution for the Buckling Load of Flat Sandwich Panels with Loaded Edges Clamped

Abstract This paper presents an exact solution in terms of infinite series of the problem of buckling by compressive forces in one direction of a rectangular plate with built-in edges (zero slope, zero displacement in the direction normal to the plane of the plate). The buckling load is calculated for 14 ratios of length to width, ranging in steps of 0.25 from 0.75 to 4. On the basis of convergence, as the number of terms used in the infinite series is increased, it is estimated that the possible error in the numerical results presented is of the order of 0.1 per cent. A comparison is given with the work of other authors.

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Wrinkling of Wide Sandwich Panels∕Beams With Orthotropic Phases by an Elasticity Approach

Journal of Applied Mechanics ◽

10.1115/1.1978919 ◽

2004 ◽

Vol 72 (6) ◽

pp. 818-825 ◽

Cited By ~ 28

Author(s):

G. A. Kardomateas

Keyword(s):

Compressive Loading ◽

Sandwich Panels ◽

Wave Mode ◽

Buckling Load ◽

Face Sheet ◽

Beam Model ◽

Elasticity Solution ◽

Short Side ◽

Euler Buckling ◽

Sandwich Construction

There exist many formulas for the critical compression of sandwich plates, each based on a specific set of assumptions and a specific plate or beam model. It is not easy to determine the accuracy and range of validity of these rather simple formulas unless an elasticity solution exists. In this paper, we present an elasticity solution to the problem of buckling of sandwich beams or wide sandwich panels subjected to axially compressive loading (along the short side). The emphasis on this study is on the wrinkling (multi-wave) mode. The sandwich section is symmetric and all constituent phases, i.e., the facings and the core, are assumed to be orthotropic. First, the pre-buckling elasticity solution for the compressed sandwich structure is derived. Subsequently, the buckling problem is formulated as an eigen-boundary-value problem for differential equations, with the axial load being the eigenvalue. For a given configuration, two cases, namely symmetric and anti-symmetric buckling, are considered separately, and the one that dominates is accordingly determined. The complication in the sandwich construction arises due to the existence of additional “internal” conditions at the face sheet∕core interfaces. Results are produced first for isotropic phases (for which the simple formulas in the literature hold) and for different ratios of face-sheet vs core modulus and face-sheet vs core thickness. The results are compared with the different wrinkling formulas in the literature, as well as with the Euler buckling load and the Euler buckling load with transverse shear correction. Subsequently, results are produced for one or both phases being orthotropic, namely a typical sandwich made of glass∕polyester or graphite∕epoxy faces and polymeric foam or glass∕phenolic honeycomb core. The solution presented herein provides a means of accurately assessing the limitations of simplifying analyses in predicting wrinkling and global buckling in wide sandwich panels∕beams.

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Critical buckling load of honeycomb sandwich panels reinforced by three-phase orthotropic skins enhanced by carbon nanotubes

Composite Structures ◽

10.1016/j.compstruct.2020.111904 ◽

2020 ◽

Vol 237 ◽

pp. 111904 ◽

Cited By ~ 4

Author(s):

Michele Bacciocchi ◽

Angelo Marcello Tarantino

Keyword(s):

Carbon Nanotubes ◽

Sandwich Panels ◽

Buckling Load ◽

Critical Buckling Load ◽

Three Phase ◽

Honeycomb Sandwich

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An exact solution for vibro-acoustic response of smart sandwich panels with MEE composite Layer

Composite Structures ◽

10.1016/j.compstruct.2022.115201 ◽

2022 ◽

pp. 115201

Author(s):

M.P. Arunkumar ◽

Vinod Bhagat ◽

Qian Geng ◽

Yueming Li ◽

Jeyaraj Pitchaimani

Keyword(s):

Exact Solution ◽

Composite Layer ◽

Sandwich Panels ◽

Acoustic Response

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Upper and Lower Bounds for Special Eigenvalues

Journal of Applied Mechanics ◽

10.1115/1.4011990 ◽

1959 ◽

Vol 26 (2) ◽

pp. 246-250

Author(s):

F. C. Appl ◽

C. F. Zorowski

Keyword(s):

Exact Solution ◽

Power Series ◽

Lower Bounds ◽

Comparison Theorem ◽

Eigenvalue Problems ◽

Buckling Load ◽

Upper And Lower Bounds ◽

Elastic Buckling ◽

Variable Section ◽

Exact Eigenvalue

Abstract A method for finding upper and lower bounds for the fundamental eigenvalue in special eigenvalue problems is presented. The method is systematic and is shown to provide convergence from above and below to the exact eigenvalue under certain conditions. The method is based on the relatively well-known enclosure or comparison theorem of Collatz, and makes use of a power series to approximate the eigenfunction. The method is applied to two examples concerning the critical-elastic buckling load of variable-section columns with pinned ends. Results for the first example compare well with the exact solution, which is known; the second example is presented as an addition to the literature.

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The Linearization of the Prebuckling State and Its Effect on the Determined Instability Loads

Journal of Applied Mechanics ◽

10.1115/1.3564770 ◽

1969 ◽

Vol 36 (4) ◽

pp. 775-783 ◽

Cited By ~ 45

Author(s):

A. D. Kerr ◽

M. T. Soifer

Keyword(s):

Exact Solution ◽

Perturbation Analysis ◽

Degrees Of Freedom ◽

Elastic System ◽

Buckling Load ◽

Nonlinear Formulation ◽

Shallow Arch ◽

Buckling Loads ◽

State Of Stress

The effect of the linearization of the prebuckled state upon the determined buckling loads is studied first on an elastic system of two degrees of freedom and then on a shallow arch subjected to a uniform lateral load; structures that exhibit a nontrivial state of stress, an upper buckling load, a lower buckling load, and a bifurcation load. For each case the exact solution of the nonlinear formulation is discussed first. Then, using the perturbation analysis, the instability loads are determined again using the exact and the linearized prebuckled state, respectively. The paper concludes with a comparison of the obtained buckling loads and a discussion of relevant problems. It was found that the usual “adjacent equilibrium” argument presented in the literature, according to which only the displacements are perturbed, is not applicable for the determination of the bifurcation pressures of the shallow arch. A proper argument is presented and then used to determine the bifurcation and limit points.

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